Question

A collar is established by buying a share of stock for $78, buying a six-month put option with exercise price $75, and writing a six-month call option with exercise price $80. Based on the volatility of the stock, you calculate that for an exercise price of $75 and maturity of six months, N(d1) = 0.6959, whereas for the exercise price of $80, N(d1) = 0.6729.

What will be the gain or loss on the collar if the stock price increases by $1? (Input the amount as a positive value. Round your answer to 3 decimal places.)

Answer 1

The gain on the collar will be $0.322 if the stock price increases by $1.

Step-by-step explanation:

A collar is a trading strategy that involves buying a share of stock, buying a put option, and writing a call option. In this case, the stock is bought for $78, the put option has an exercise price of $75, and the call option has an exercise price of $80.

If the stock price increases by $1, the put option will expire worthless, as the exercise price is higher than the stock price. The gain on the collar will be the increase in the stock price minus the decrease in the call option value.

Since the stock price increases by $1, the call option value decreases by $1 ($1 x (N(d1) - N(d2)), where d1 = 0.6959 and d2 = 0.6729).

Therefore, the gain on the collar will be $1 - $1 x (N(d1) - N(d2)) = $0.322.

Answer 2

To calculate the gain or loss on the collar if the stock price increases by $1, we need to consider the different components of the collar strategy. The collar involves buying a share of stock, buying a put option, and writing a call option. The total gain or loss on the collar can be calculated by subtracting the losses from the gain.

Step-by-step explanation:

To calculate the gain or loss on the collar if the stock price increases by $1, we need to consider the different components of the collar strategy. The collar involves buying a share of stock, buying a put option, and writing a call option.

If the stock price increases by $1, the value of the stock will increase by $1. However, the gain on the stock will be offset by the loss on the put option and the call option.

Let's calculate the gain or loss on each component:

1. Stock: Since the stock price increases by $1, the gain on the stock will be $1.
2. Put Option: The put option has an exercise price of $75. If the stock price is above $75, the put option will expire worthless, resulting in a loss of the premium paid for the put option.
3. Call Option: The call option has an exercise price of $80. If the stock price is above $80, the call option will be exercised and the writer of the option will be obligated to sell the stock at $80. This will result in a loss equal to the difference between the exercise price and the current stock price.

Based on the given information, the probability of the stock price being above $75 is N(d1) = 0.6959, and the probability of the stock price being above $80 is N(d1) = 0.6729.

Using this information, we can calculate the gain or loss on the collar:

1. Stock Gain: $1
2. Put Option Loss: $0.6959 * $75 (premium paid for the put option)
3. Call Option Loss: $0.6729 * ($80 - current stock price)

The total gain or loss on the collar can be calculated by subtracting the losses from the gain:

Total Gain/Loss on Collar: $1 - ($0.6959 * $75) - ($0.6729 * ($80 - current stock price))